id:A158387 - OEIS Search Results

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a(n) = sign of parity of number of divisors of n.

+0
1

-1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1 (list; graph; listen)

	OFFSET	`1,1`
	COMMENT	`a(n) = (-1)^tau(n) = (-1)^A000005. a(1) = -1, a(p) = 1, a(pq) = 1, a(pq...z) = 1, a(p^k) = (-1)^(k+1), for p = primes (A000040), pq = product of two distinct primes (A006881), pq...z = product of k (k > 2) distinct primes p, q, ..., z (A120944), p^k = prime powers (A000961(n) for n > 1), k = natural numbers (A000027).`
	EXAMPLE	`a(12) = (-1)^6 = 1.`
	CROSSREFS	`Cf.: A000005, A000040, A006881, A120944, A000961, A000027.` `Sequence in context: A157895 A063747 A077008 this_sequence A087960 A164660 A114523` `Adjacent sequences: A158384 A158385 A158386 this_sequence A158388 A158389 A158390`
	KEYWORD	`sign`
	AUTHOR	`Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 17 2009`

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Last modified December 17 13:29 EST 2009. Contains 170826 sequences.

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